Feeding Frenzy

At the title screen you have a number of options. Choose adventure. Leon's levels are levels 9-16 of the game. Complete them and you'll net yourself the achievement. If you die during this process and run out of continues (somehow...) you can return to the level you last completed and continue from there, with your score reset. The achievement will still unlock though after the completion of the levels, despite how many tries it takes you.

Beat the first 16 levels of the game